A comparison of the history effects in weakly pinned single crystals of a high T-c YBa2Cu3O7-delta (for H parallel to c) and a low T-c Ca3Rh4Sn13, which show anomalous variations in critical current density J(c)(H), is presented via the tracings of the minor magnetization hysteresis loops using a vibrating sample magnetometer. The sample histories focussed are: (i) the field cooled (FC), (ii) the zero field cooled (ZFC) and (iii) an isothermal reversal of field from the normal state. An understanding of the results in terms of the modulation in the plastic deformation of the elastic vortex solid and supercooling across the order-disorder transitions is sought.